Technical Review No 1.
Experimental Modal Analysis and Operational Modal
Everything vibrates! This is a fact of life and modal analysis is the
technique used to characterize how structures behave dynamically.
Modal analysis separates the complicated vibration pattern that can be
measured in a physical domain using e.g. accelerometers into a set of modes
of vibration. These modes are actually the “finger print” of a structure.
mode of vibration is characterized by the following three modal parameters:
Natural Frequency, fi.
This value is typically given in Hertz (Hz).
ζi. This value is typically represented as a
percentage of the critical damping and therefore given in percent (%)
φi. The geometrical way the structure moves in this
particular mode of vibration.
shown in the figure above a structure typically has many modes of vibration.
As the modes get higher and higher in frequency they normally also get more
and more complicated modes shapes and it normally require more energy to
excite these modes compared to the more simple low frequency modes
Experimental Modal Analysis
For decades it has been possible to estimate the modes of vibration of small
structures that could be taken to a laboratory and mounted in a so-called
Test Rig. The Test-Rig is necessary, because the structure is not allowed to
be excited by anything except some artificial excitation that can be
1.2.1 Impact Hammers and Shakers
The excitation is normally produced by
either an Impact Hammer or by one or more shakers. Both these types of
devices can produce a force and at the same time measure it. The figure
below demonstrate how a typically setup for an Experimental Modal Analysis
(EMA) is. The structure is hanging freely in a test rig, and one or more
accelerometers are mounted in the positions where the response of the modes
of interest is good. The impact hammer is used to impact the structure in
all the positions where the modes shapes is needed. If a single
accelerometer is used to measure the response the technique is normally
called Single Reference technique, whereas in the case of several it is
referred to as Multiple (Poly) Reference techniques.
If one or more shakers are used they will be mounted in positions where the
modes of interest can be excited by them. Now it is one or more
accelerometers that are moved around on the structure from measurement to
measurement. Shakers are normally used for larger structures that cannot
easily be excited, or if a specific input signal is desired.
Modal analysis (EMA) – A Well-proven Technique for Small Structures
1.2.2 Frequency Response Function
During the test there will be several sets of simultaneous measurements of
the input forces and the output accelerations. These signals are transferred
to the frequency domain by the so-called Fast Fourier Transform (FFT) that
produces an input force spectrum and an output acceleration spectrum. The
trick now is to divide the output spectrum with the input spectrum to obtain
the so-called Frequency Response Function (FRF). This function shows how the
structure will respond to input at a certain frequency. It is a system
function that is in principle very clean, since all input is divided out of
To keep the FRF clean it is very important that only the measurable force is
the only excitation acting on the structure during the test. Any unmeasured
input forces will cause a pollution of the FRF. The Coherence Function is
normally used to evaluate the quality of the FRF.
1.2.3 Curve-fitting Modes from Frequency
Once the clean Frequency Response Function is obtained modes are normally
estimated using various curve-fitting methods, that either estimates a
single or multiple modes at the same time. If only a few modes are estimated
the estimators are termed Narrow-banded curve-fitter, whereas if
the frequency range is broad, the methods are referred to Broad-banded
1.2.4 Limitations of Experimental Modal Analysis
There are cases where the Experimental Modal Analysis have difficulties in
provided the expected results. It is interesting to list these as it
explains why there is a need for complimentary Operational Modal Analysis
tools. The limitations can be summarized in the follow list:
excitation during testing – Test Rig Required!
It is absolutely not allowed that any excitation that cannot be measured
is exciting the structure. This will deteriorate the Frequency Response
Function and therefore the modes being estimated from it.
have to be accepted sometimes.
Since the structure needs to hang freely in a Test Rig the boundary
conditions of it might change significantly. This will change all modal
parameters obtained in this condition compared to if the structure was
tested in situ.
levels and operating conditions have to be accepted sometimes.
Similar to the problems with the boundaries it can also be problematic
with the applied excitation, since it might be very different from the
excitation that the structure will experience in situ. If the structure
is slightly non-linear in its behavior, then the modal parameters will
change. Also if e.g. temperatures are very different in situ compared to
the test especially the natural frequencies will be estimated
Hammers and shakers
Both in case of symmetric structures as well as large structures it
might be difficult to excite the structures artificially in a way that
is effective for the mode estimation.
1.3 Operational Modal Analysis for In-situ Testing
In many cases it is not possible to apply the
well-proven Experimental Modal Analysis. Some examples are:
Large structures, such as high rise buildings,
bridges, towers and dams.
Rotating machinery, such as wind turbines,
generators, engines and pumps.
Maritime structures, such as ships,
submarines and offshore platforms.
In general for all these structures are that they
are being subjected to some external uncontrollable in-situ forces that
cause them to vibrate. Since these forces in general cannot be measured it
is impossible to apply the Experimental Modal Analysis techniques that rely
on the estimation of the clean Frequency Response Function.
The only thing that still can be obtained from an
operating structure is the response due to the unknown excitation forces.
This response is typically measured in a number of positions that is
referred to as the Degrees Of Freedom (DOF). It is in these points
that the modes shapes ultimately are determined.
The response is typically measured with
accelerometers, but there is no reason not to use other devices that can
measure dynamic response. The response can as such also be measured with
laser vibrometers or strain gauges.
1.3.1 The Framework of Operational Modal Analysis
The major difference to Experimental Modal Analysis
performed in a laboratory is that some or all of the excitation forces are
unknown in case of in-situ Operational Modal Analysis.
This means that the theoretically framework in
Operational Modal Analysis needs to be something different from the
completely known (deterministic) input output relation – The Frequency
Response Function. It is now necessary to assume something about the unknown
excitation forces. When something need to be assumed the theoretically
framework shifts to a stochastic framework where the input now is assumed to
be a so-called stochastic process.
The stochastic framework used in Operational Modal Analysis
The stochastic framework used in Operational Modal Analysis assumes that the
excitation that is driving the system is a so-called Gaussian White
Noise Stochastic Process. This can be translated to more human language
as an excitation input that has the same energy level at all frequencies we
are looking at. So it means that this assumption alone imply that all modes
are excited equally.
However, normally this is not the case in the real world as there is always
input at some frequencies that contains more energy than others. To
compensate for this, the unknown excitation forces being modeled in be this
stochastic framework are assumed to be the result of a “shaping” done to the
white noise. The shaping is assumed to be made by a linear filter that can
shape the flat white noise into the correct shape having an energy
distribution like the true unknown excitation forces.
So the response of a structure is in this framework assumed to be the output
of a combined system composed by the structural system containing the
dynamics of the structure being tested as well as the excitation filter that
outputs the unknown excitation forces that we cannot measure.
In practice the above theory imply that the excitation needed in order to
perform Operational Modal Analysis must be broad-banded in the
frequency range of the modes of interest. If there is nothing that
persistently excites the modes during the test the result will be very poor.
It is acceptable to have very narrow-banded excitation, such as
harmonic excitation, as well but there still have to be broad-banded
excitation at the same time.
Another practical implication of the above framework is that some of the
“modes” appearing in the measured response might not originate from the
structure itself. It might actually be input “modes” that have been filtered
through the structural system. In practice it means that e.g. some peaks of
the spectra might not relate to the structure but to the input.
1.3.2 Practical Measurement Procedures
Basically there are two ways to measure in order to obtain the response
needed for Operation Modal Analysis. Either all sensors are mounted once and
the measurements are made, or the sensors are moved from position to
position and multiple measurements are made.
When the available sensors are positioned this is referred to as being a
Test Setup. A measurement made for this position of the sensors is
called a Data Set. So, if the measurement is repeated for a
particular Test Setup, it is simply a new Data Set. Either a single data set
is used for the modal analysis or one or more of them are merged together to
form longer records of data.
Single Test Setup Measurement Procedure
There are cases where it is undesirable to move around with the sensors. In
these cases sensors are placed ones in a Single Test Setup. The
cases where this approach is in use is e.g. in permanent monitoring systems
or in cases where the measurement cannot be repeated or simply to save time.
Multiple Test Setups Measurement Procedure
In many cases though the sensors are moved around from one set of positions
to another set. This is called a Multiple Test Setups measurement
Multiple Test Setup measurement procedure
In this case a few high quality sensors are placed in
positions where the modes of interest are having a good response level. These
sensors are called reference sensors and are fixed in the same position when
moving from one Test Setup to another. The rest of the sensors are placed in the
DOF positions where mode shapes is wanted.
As the reference sensors are staying in the same
positions they are basically measuring the mode shapes in these positions over
and over. Since these mode shapes part should be the same from one Test Setup to
the next, it provides a way to adjust the rest of the mode shape values of the
different Test Setups. Normally, the adjustment is performed with some least
squares fitting technique, in order to make use of the multiple references
It is extremely important that the reference sensors
are positioned so that the mode shapes of the modes of interest have good
amplitude in at least one of the references. Since it can be problematic to find
a single position where this is the case, then recommendation is to use several
references sensors in different directions and positions.
Operational Modal Analysis is not a substitute of
Experimental Modal Analysis but should be considered a complimentary tool for
the vast number of cases where the input foces cannot be controlled or measured.
There will still be many cases where Experimental Modal
Analysis is the right tool, such as prototype testing of small structures where
it is important to have same testing conditions from test to test.
However, there are just many cases where it is
impossible to create such homogene conditions, especially is if structures are
larger and if the excitation primarely is mother nature.